3+1 formalism and bases of numerical relativity - LUTh ...
3+1 formalism and bases of numerical relativity - LUTh ... 3+1 formalism and bases of numerical relativity - LUTh ...
212 BIBLIOGRAPHY [195] S. Nissanke : Post-Newtonian freely specifiable initial data for binary black holes in numerical relativity, Phys. Rev. D 73, 124002 (2006). [196] N. Ó Murchadha and J.W. York : Initial-value problem of general relativity. I. General formulation and physical interpretation, Phys. Rev. D 10, 428 (1974). [197] R. Oechslin, H.-T. Janka and A. Marek : Relativistic neutron star merger simulations with non-zero temperature equations of state I. Variation of binary parameters and equation of state, Astron. Astrophys., submitted [preprint: astro-ph/0611047]. [198] R. Oechslin, K. Uryu, G. Poghosyan, and F. K. Thielemann : The Influence of Quark Matter at High Densities on Binary Neutron Star Mergers, Mon. Not. Roy. Astron. Soc. 349, 1469 (2004). [199] K. Oohara, T. Nakamura, and M. Shibata : A Way to 3D Numerical Relativity, Prog. Theor. Phys. Suppl. 128, 183 (1997). [200] L.I. Petrich, S.L Shapiro and S.A. Teukolsky : Oppenheimer-Snyder collapse with maximal time slicing and isotropic coordinates, Phys. Rev. D 31, 2459 (1985). [201] H.P. Pfeiffer : The initial value problem in numerical relativity, in Proceedings Miami Waves Conference 2004 [preprint gr-qc/0412002]. [202] H.P. Pfeiffer and J.W. York : Extrinsic curvature and the Einstein constraints, Phys. Rev. D 67, 044022 (2003). [203] H.P. Pfeiffer and J.W. York : Uniqueness and Nonuniqueness in the Einstein Constraints, Phys. Rev. Lett. 95, 091101 (2005). [204] T. Piran : Methods of Numerical Relativity, in Rayonnement gravitationnel / Gravitation Radiation, edited by N. Deruelle and T. Piran, North Holland, Amsterdam (1983), p. 203. [205] E. Poisson : A Relativist’s Toolkit, The Mathematics of Black-Hole Mechanics, Cambridge University Press, Cambridge (2004); http://www.physics.uoguelph.ca/poisson/toolkit/ [206] F. Pretorius : Numerical relativity using a generalized harmonic decomposition, Class. Quantum Grav. 22, 425 (2005). [207] F. Pretorius : Evolution of Binary Black-Hole Spacetimes, Phys. Rev. Lett. 95, 121101 (2005). [208] F. Pretorius : Simulation of binary black hole spacetimes with a harmonic evolution scheme, Class. Quantum Grav. 23, S529 (2006). [209] T. Regge and C. Teitelboim : Role of surface integrals in the Hamiltonian formulation of general relativity, Ann. Phys. (N.Y.) 88, 286 (1974). [210] B. Reimann and B. Brügmann : Maximal slicing for puncture evolutions of Schwarzschild and Reissner-Nordström black holes, Phys. Rev. D 69, 044006 (2004).
BIBLIOGRAPHY 213 [211] B.L. Reinhart : Maximal foliations of extended Schwarzschild space, J. Math. Phys. 14, 719 (1973). [212] A.D. Rendall : Theorems on Existence and Global Dynamics for the Einstein Equations, Living Rev. Relativity 8, 6 (2005); http://www.livingreviews.org/lrr-2005-6 [213] O.A. Reula : Hyperbolic Methods for Einstein’s Equations, Living Rev. Relativity 1, 3 (1998); http://www.livingreviews.org/lrr-1998-3 [214] O. Reula : Strong Hyperbolicity, lecture at the VII Mexican School on Gravitation and Mathematical Physics (Playa del Carmen, November 26 - December 2, 2006, Mexico); available at http://www.smf.mx/ ∼ dgfm-smf/EscuelaVII [215] M. Saijo : The Collapse of Differentially Rotating Supermassive Stars: Conformally Flat Simulations, Astrophys. J. 615, 866 (2004). [216] M. Saijo : Dynamical bar instability in a relativistic rotational core collapse, Phys. Rev. D 71, 104038 (2005). [217] O. Sarbach and M. Tiglio : Boundary conditions for Einstein’s field equations: mathematical and numerical analysis, J. Hyper. Diff. Equat. 2, 839 (2005). [218] G. Schäfer : Equations of Motion in the ADM Formalism, lectures at Institut Henri Poincaré, Paris (2006), http://www.luth.obspm.fr/IHP06/ [219] M.A. Scheel, H.P. Pfeiffer, L. Lindblom, L.E. Kidder, O. Rinne, and S.A. Teukolsky : Solving Einstein’s equations with dual coordinate frames, Phys. Rev. D 74, 104006 (2006). [220] R. Schoen and S.-T. Yau : Proof of the Positive Mass Theorem. II., Commun. Math. Phys. 79, 231 (1981). [221] Y. Sekiguchi and M. Shibata : Axisymmetric collapse simulations of rotating massive stellar cores in full general relativity: Numerical study for prompt black hole formation, Phys. Rev. D 71, 084013 (2005). [222] S.L. Shapiro and S.A. Teukolsky : Collisions of relativistic clusters and the formation of black holes, Phys. Rev. D 45, 2739 (1992). [223] M. Shibata : Relativistic formalism for computation of irrotational binary stars in quasiequilibrium states, Phys. Rev. D 58, 024012 (1998). [224] M. Shibata : 3D Numerical Simulations of Black Hole Formation Using Collisionless Particles, Prog. Theor. Phys. 101, 251 (1999). [225] M. Shibata : Fully General Relativistic Simulation of Merging Binary Clusters — Spatial Gauge Condition, Prog. Theor. Phys. 101, 1199 (1999).
- Page 162 and 163: 162 Choice of foliation and spatial
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- Page 180 and 181: 180 Evolution schemes Now the ∇-d
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- Page 184 and 185: 184 Evolution schemes = 1 2 −∆
- Page 186 and 187: 186 Evolution schemes corresponds t
- Page 188 and 189: 188 Evolution schemes
- Page 190 and 191: 190 Lie derivative Figure A.1: Geom
- Page 192 and 193: 192 Lie derivative
- Page 194 and 195: 194 Conformal Killing operator and
- Page 196 and 197: 196 Conformal Killing operator and
- Page 198 and 199: 198 Conformal Killing operator and
- Page 200 and 201: 200 BIBLIOGRAPHY [13] A. Anderson a
- Page 202 and 203: 202 BIBLIOGRAPHY [43] T.W. Baumgart
- Page 204 and 205: 204 BIBLIOGRAPHY [75] M. Campanelli
- Page 206 and 207: 206 BIBLIOGRAPHY [105] G. Darmois :
- Page 208 and 209: 208 BIBLIOGRAPHY [135] H. Friedrich
- Page 210 and 211: 210 BIBLIOGRAPHY [163] J. Isenberg
- Page 214 and 215: 214 BIBLIOGRAPHY [226] M. Shibata :
- Page 216 and 217: 216 BIBLIOGRAPHY [255] K. Taniguchi
- Page 218 and 219: Index 1+log slicing, 161 3+1 formal
- Page 220: 220 INDEX Ricci identity, 18 Ricci
BIBLIOGRAPHY 213<br />
[211] B.L. Reinhart : Maximal foliations <strong>of</strong> extended Schwarzschild space, J. Math. Phys. 14,<br />
719 (1973).<br />
[212] A.D. Rendall : Theorems on Existence <strong>and</strong> Global Dynamics for the Einstein Equations,<br />
Living Rev. Relativity 8, 6 (2005);<br />
http://www.livingreviews.org/lrr-2005-6<br />
[213] O.A. Reula : Hyperbolic Methods for Einstein’s Equations, Living Rev. Relativity 1, 3<br />
(1998);<br />
http://www.livingreviews.org/lrr-1998-3<br />
[214] O. Reula : Strong Hyperbolicity, lecture at the VII Mexican School on Gravitation <strong>and</strong><br />
Mathematical Physics (Playa del Carmen, November 26 - December 2, 2006, Mexico);<br />
available at http://www.smf.mx/ ∼ dgfm-smf/EscuelaVII<br />
[215] M. Saijo : The Collapse <strong>of</strong> Differentially Rotating Supermassive Stars: Conformally Flat<br />
Simulations, Astrophys. J. 615, 866 (2004).<br />
[216] M. Saijo : Dynamical bar instability in a relativistic rotational core collapse, Phys. Rev.<br />
D 71, 104038 (2005).<br />
[217] O. Sarbach <strong>and</strong> M. Tiglio : Boundary conditions for Einstein’s field equations: mathematical<br />
<strong>and</strong> <strong>numerical</strong> analysis, J. Hyper. Diff. Equat. 2, 839 (2005).<br />
[218] G. Schäfer : Equations <strong>of</strong> Motion in the ADM Formalism, lectures at Institut Henri<br />
Poincaré, Paris (2006), http://www.luth.obspm.fr/IHP06/<br />
[219] M.A. Scheel, H.P. Pfeiffer, L. Lindblom, L.E. Kidder, O. Rinne, <strong>and</strong> S.A. Teukolsky :<br />
Solving Einstein’s equations with dual coordinate frames, Phys. Rev. D 74, 104006 (2006).<br />
[220] R. Schoen <strong>and</strong> S.-T. Yau : Pro<strong>of</strong> <strong>of</strong> the Positive Mass Theorem. II., Commun. Math. Phys.<br />
79, 231 (1981).<br />
[221] Y. Sekiguchi <strong>and</strong> M. Shibata : Axisymmetric collapse simulations <strong>of</strong> rotating massive<br />
stellar cores in full general <strong>relativity</strong>: Numerical study for prompt black hole formation,<br />
Phys. Rev. D 71, 084013 (2005).<br />
[222] S.L. Shapiro <strong>and</strong> S.A. Teukolsky : Collisions <strong>of</strong> relativistic clusters <strong>and</strong> the formation <strong>of</strong><br />
black holes, Phys. Rev. D 45, 2739 (1992).<br />
[223] M. Shibata : Relativistic <strong>formalism</strong> for computation <strong>of</strong> irrotational binary stars in<br />
quasiequilibrium states, Phys. Rev. D 58, 024012 (1998).<br />
[224] M. Shibata : 3D Numerical Simulations <strong>of</strong> Black Hole Formation Using Collisionless<br />
Particles, Prog. Theor. Phys. 101, 251 (1999).<br />
[225] M. Shibata : Fully General Relativistic Simulation <strong>of</strong> Merging Binary Clusters — Spatial<br />
Gauge Condition, Prog. Theor. Phys. 101, 1199 (1999).
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